Off-screen can be used to describe events in a movie or tv show. For example,
"Harry's father dies off-screen"
What term or phrase can I use if I'm talking about events in a book?
"Harry's father dies ----"
Same question for on-screen.
Before we had the (silver) screen, we had a stage.
Something that was not visible to the audience happened offstage, which freedictionary describes as:
adj. 1. Situated or taking place in the area of a stage that is invisible to the audience.
adv. 2.b. Behind the scenes; not visible to the public: The meetings between the leaders took place offstage.
I see no problem applying this to a book, the stage idiom being quite commonly understood and quite adaptable (offstage can also refer to non-theater settings, meaning in private, as opposed to the part of one's life that takes place “in the spotlights”.)
That's a good question, and one for which I've never heard the answer (at least that I can recall). You could perhaps describe this as events occurring "outside the narrative or discourse."
Harry's father dies in a /sidestory/back scene/, off the main narrative /flow/.
Harry's father dies in a /backstory/back scene/, off the main narrative flow.*
Also, one could consider
off-camera, just as good as the "off-stage" mentioned by others